Dr. Lam's research interest is on the structural and representation theory of vertex operator algebras and their applications to the theory of sporadic simple groups. In particular, he is interested in a special vertex operator algebra called Moonshine vertex operator algebra whose full automorphism group is the Monster simple group.
- Ph.D. Ohio State University 1996
- B.A. (2nd class honour, division 1) University of Hong Kong 1989
- B.A. University of Hong Kong
- Deputy Director Institute of Mathematics, Academia Sinica 2013/8 - 2019/11
- Research Fellow Academia Sinica, Taiwan 2009 - Present
- Professor National Cheng Kung University 2004 - 2009
- Associate Professor National Cheng Kung University 2001 - 2004
- Assistant Professor National Cheng Kung University 2000 - 2001
- Research Associate University of Tsukuba 1997 - 2000
- Lecturer Ohio State University 1996 - 1997
- 2009-2011, Outstanding Research Award, National Science Council, Taiwan, R.O.C.
- 2008, Distinguished Professor, National Cheng Kung University
- (with Cuipo Jiang, Hiroshi Yamauchi) "The classification of vertex operator algebras of OZ-type generated by Ising vectors of $\sigma$-type", 2024 , Link
- (with Hsian-Yang Chen) "Completely fixed point free isometry and cyclic orbifold of lattice vertex operator algebras", Journal of Algebra, 2024 , Link
- (with Hiroki Shimakura) "Extra automorphisms of cyclic orbifolds of lattice vertex operator algebras", Journal of Pure and Applied Algebra , 228, 2024 , Link
- (with Drazen Adamovic, Veronika Pedic Tomic, Nina Yu) "On irreducibility of modules of Whittaker type: twisted modules and nonabelian orbifolds", 2023 , Link
- (with Masahiko Miyamoto) "A lattice theoretical interpretation of generalized deep holes of the Leech lattice vertex operator algebra", Forum of Mathematics, Sigma, 11 (e86), 2023 , Link
- "Unitary forms for holomorphic vertex operator algebras of central charge 24", Letters in Mathematical Physics, 113 (2), 2023 , Link, Link
- (with Koichi Betsumiya, Hiroki Shimakura) "Automorphism Groups and Uniqueness of Holomorphic Vertex Operator Algebras of Central Charge 24", Communications in Mathematical Physics , 399 (3), 1773-1810, 2023 , Link, Link
- (with Naoki Chigira, Masahiko Miyamoto) "Orbifold construction and Lorentzian construction of Leech lattice vertex operator algebra", J. Algebra, 593, 26-71, 2022-03 , Link
- (with Hiroshi Yamauchi) "The Conway-Miyamoto correspondences for the Fischer 3-transposition groups", Transactions of American Mathematical Society , 375 (3), 2025-2067, 2022-03 , Link
- (with Koichi Betsumiya, Hiroki Shimakura) "Automorphism groups of cyclic orbifold vertex operator algebras associated with the Leech lattice and some non-prime isometries", Israel Journal of Mathematics, 2022
- (with Hiromichi Yamada) "Sigma involutions associated with parafermion vertex operator algebra $K(sl_2,k)$", Linear and Multilinear Algebra, 70 (21), 6780-6819, 2022 , Link
- (with Hsian-Yang Chen) "Fourvolutions and automorphism groups of orbifold lattice vertex operator algebras", Taiwanese J. Math. , 25 (6), 1173-1185, 2021-12 , Link, Link
- (with Jethro van Ekeren, Sven Möller, Hiroki Shimakura) "Schellekens' list and the very strange formula", Advances in Mathematics, 380, 2021-03 , Link
- (with J. Connor Grady, James E. Tener, Hiroshi Yamauchi) "Classification of extremal vertex operator algebras with two simple modules", Journal of Mathematical Physics, 61 (5), 2020 , Link
- (with Lin, Xingjun) "A holomorphic vertex operator algebra of central charge 24 with the weight one Lie algebra $F_{4,6}A_{2,2}$", J. Pure Appl. Algebra, 224 (3), 1241-1279, 2020 , Link
- "Cyclic orbifolds of lattice vertex operator algebras having group-like fusions", Letters in Mathematical Physics, 110 (5), 1081-1112, 2020 , Link, Link
- (with Hiroki Shimakura) "Inertia groups and uniqueness of holomorphic vertex operator algebras", Transformation groups, 25 (4), 1223-1268, 2020 , Link, Link
- (with H. Shimakura) "On orbifold constructions associated with the Leech lattice vertex operator algebra", Mathematical Proceedings of the Cambridge Philosophical Society. , 168 (2), 261-285, 2020 , Link
- (with Hiroki Shimakura) "Reverse orbifold construction and uniqueness of holomorphic vertex operator algebras", Trans. Amer. Math. Soc., 372 (10), 7001-7024, 2019-11 , Link
- (with T. Arakawa, H. Yamada) "Parafermion vertex operator algebras and W-algebras", Trans. Amer. Math. Soc., 371 (6), 4277-4301, 2019-03 , Link
- (with D. Adamovic, V. Pedić, N. Yu ) "On irreducibility of modules of Whittaker type for cyclic orbifold vertex algebras", J. Algebra, 539, 1-23, 2019
- (with C. P. Jiang, H. Yamauchi) "Vertex operator algebras generated by Ising vectors of $\sigma$-type", Mathematische Zeitschrift , 293 (1月2日), 425-442, 2019 , Link
- (with C. P. Jiang) "Level-Rank Duality for Vertex Operator Algebras of types B and D", Bull. Inst. Math. Acad. Sin. (N.S.), 14 (1), 31-54, 2019 , Link, Link
- (with Hiroshi Yamauchi) "3-dimensional Griess algebras and Miyamoto involutions", Bull. Inst. Math. Acad. Sin. (N.S.), 14 (2), 119-147, 2019 , Link, Link
- (with T. Abe, H. Yamada) "On $\mathbb{Z}_p$-orbifold constructions of the Moonshine vertex operator algebra", Mathematische Zeitschrift, 290 (1), 683-, 2018-10 , Link, Link
- (with T. Abe, H. Yamada) "Extensions of tensor products of $\mathbb{Z}_p$-orbifold models of the lattice vertex operator algebra $V_{\sqrt{2}A_{p-1}}$", J. Algebra , 510, 24-, 2018 , Link
- (with Hsian-Yang Chen, Hiroki Shimakura) "$\mathbb{Z}_3$-orbifold construction of the Moonshine vertex operator algebra and some maximal 3-local subgroups of the Monster", Mathematische Zeitschrift, 288 (1月2日), 75-, 2018 , Link, Link
- (with Kazuya Kawasetsu, Xingjun Lin) "$\mathbb{Z}_2$-orbifold construction associated with $(−1)$-isometry and uniqueness of holomorphic vertex operator algebras of central charge 24", Proceedings of Amer. Math. Soc. , 146 (5), 1937-1950, 2018 , Link
- (with H.Y. Chen ) "Quantum dimensions and fusion rules of the VOA $V_{L_{C\times D}}^\tau$", Journal of Algebra, 459, 309-349, 2016-08 , Link
- (with H. Shimakura) "Orbifold construction of holomorphic vertex operator algebras associated to inner automorphisms", Communications in Mathematical Physics, 342 (3), 803-841, 2016-03 , Link
- (with H. Shimakura) "A holomorphic vertex operator algebras of central charge 24 whose weight one Lie algebra has type $A_{6,7}$", Letters in Mathematical Physics, 106, 1575-1585, 2016 , Link, Link
- (with C.S. Su) "Griess algebras generated by the Griess algebras of two 3A-algebras with a common axis", J. Math Soc. Japan, 67 (2), 453-476, 2015-04
- (with R.L. Griess Jr.) "Groups of Lie Type, Vertex Algebras, and Modular Moonshine", International Mathematics Research Notices, 2015 , Link
- (with H. Shimakura) "Classification of holomorphic framed vertex operator algebras of central charge 24", Amer. J. Math, 137 (1), 111-137, 2015
- (with H. Yamauchi) "On 3-transposition groups generated by $\sigma$-involutions associated to $c=4/5$ Virasoro vectors", J. Algebra, 416, 84-121, 2014
- (with H.Y. Chen) "An explicit Majorana representation of the group $3^2{:}2$ of $3C$-pure type ", Pacific Journal of Mathematics , 271 (1), 25-51, 2014
- (with Hsian Yang Chen) "Weyl groups and vertex operator algebras generated by Ising vectors satisfying $(2B,3C)$ condition", Rev. Math. Phys. , 26 (6), 2014
- "A level-rank duality for parafermion vertex operator algebras of type A", Proc. Amer. Math. Soc., 142 (12), 4133-4142, 2014
- (with T. Arakawa, H. Yamada) " Zhu's algebras, $C_2$-algebras and $C_2$-cofiniteness of parafermion vertex operator algebras", Adv. Math. , 264, 261-295, 2014
- (with H.Y. Chen) "Coset Construction of $\mathbb{Z}/3$ orbifold vertex operator algebra $V_{\sqrt{2}A_2}^\tau$", J. Pure and Applied Algebra, 218 (1), 148-173, 2014
- (with C.S. Su) "Griess algebras generated by 3 Ising vectors of central 2A-type", J. algebra, 374, 141-166, 2013
- (with R.L. Griess) "Moonshine paths for $3A$ and $6A$ nodes of the extended $E_8$-diagram", J. Algebra, 379, 85-112, 2013
- (with Masaaki Harada; Akihiro Munemasa) "Residue codes of extremal Type II $\mathbb{Z}_4$-codes and the moonshine vertex operator algebra", Math. Z. , 274 (1), 685-700, 2013
- (with Robert L.~Griess Jr.) "A new existence proof of the Monster by VOA theory", Michigan Mathematical Journal, 61, 555-573, 2012 , Link
- (with R.L. Griess, Jr. ) "Diagonal lattices and rootless $EE_8$ pairs", J. Pure and Applied Algebra, 216 (1), 154-169, 2012
- (with H. Shimakura) "Quadratic spaces and holomorphic framed vertex operator algebras of central charge 24", Proceedings of the London Mathematical Society, 104 (3), 540-576, 2012
- (with G. Hoehn, H. Yamauchi) "McKay's $E_6$ observation on the largest Fischer group", Comm. Math. Phys. , 310, 329-365, 2012
- (with Gerald Hoehn; Hiroshi Yamauchi) "McKay's $E_7$ observations on the Baby Monster ", Inter. Math. Res. Not. , 2012, 166-212, 2012
- "On the constructions of holomorphic vertex operator algebras of central charge 24", Comm. Math. Phys., 305 (1), 153-198, 2011
- (with Robert L. Griess Jr.) "A moonshine path for $5A$ and associated lattices of ranks 8 and 16", J. Algebra, 331, 338-361, 2011
- (with R. L. Griess ) "A moonshine path from $E_8$ to the Monster", J. Pure and Applied Algebra, 215, 927-948, 2011
- (with R.L. Griess Jr.) "Dihedral groups and Sums of $EE_8$-lattices", Pure and applied mathematics quarterly, 7 (3), 621-743, 2011
- (with C. Dong, Q. Wang and H. Yamada) "The structure of parafermion vertex operator algebras", J. Algebra, 323 (2), 371-381, 2010
- (with C. Dong,and H. Yamada) "W-algebras related to parafermion algebras", J. Algebra, 332, 2236-2043, 2009
- (with H. Shimakura) "Frame Stabilizers for Framed Vertex Operator Algebras Associated to Lattices Having 4-Frames", Int. Math. Res. Notices, 2009, 4547-4577, 2009
- (with S. Sakuma) "On a class of vertex operator algebras having a faithful $S_{n+1}$-action", Taiwanese J. Math, 12 (9), 2465-2488, 2008 , Link
- (with R.L. Griess Jr.) "Rootless pairs of EE8-lattices", Electronic Research Announcements in Mathematical Sciences, 15, 52-61, 2008
- (with C. Dong,and H. Yamada) "W-algebras in lattice vertex operator algebras, in Lie Theory and Its Applications in Physics VII, ed. by H.-D. Doebner and V. K. Dobrev, Proc. of the VII International Workshop", Varna, Bulgaria, 2007 (35), 25-35, 2008
- (with H. Yamauchi) "On the structure of framed vertex operator algebras and their pointwise frame stabilizers", Commun. Math. Phys., 277 (1), 237-285, 2008
- (with H. Shimakura) "Ising vectors in the vertex operator algebra $V_{\Lambda}^+$ associated with the Leech lattice Λ", Intern. Math. Res., 2007, 2007
- (with H. Yamauchi) "A characterization of the moonshine vertex operator algebra by means of Virasoro frames", Intern. Math. Res. Notices, 2007, 2007
- (with T. S. Chen) "Extension of the tensor product of unitary Virasoro vertex operator algebras", Communications in Algebras, 35 (8), 2487-2505, 2007
- (with C. Dong, R. L. Griess) "Uniqueness results of Frenkel–Lepowsky -Meurman's moonshine vertex operator algebra", American Journal of Mathematics, 129 (2), 583-609, 2007
- (with S. Sakuma and H. Yamauchi) "Ising vectors and automorphism groups of commutant subalgebras related to root systems", Mathematische Zeitschrift, 255 (3), 597-626, 2007
- (with H. Yamada and H. Yamauchi) "Vertex operator algebra, extended E8 diagram and McKay’s observation on the Monster simple group", Transactions of American Mathematical Society, 359 (9), 4107-4123, 2007
- (with M. Miyamoto) "Niemeier Lattices, Coxeter elements and McKay's E8 observation on the Monster simple group", Intern. Math. Res. Notices, 2006
- (with H. Yamada, and H. Yamauchi) "McKay's observation and vertex operator algebras generated by two conformal vectors of central charge 1/2", Intern. Math. Res. Paper, 117-181, 2005
- (with Yamada H) "Tricritical 3-state Potts model and vertex operator algebras constructed from ternary codes", Communications in Algebra, 32 (11), 4197-4219, 2004
- (with C. Dong, K. Tanabe, H. Yamada, and K. Yokoyama) "$\mathbb{Z}_3$ symmetry and $W_3$ algebra in lattice vertex operator algebras", Pacific Journal of Mathematics, 215 (5), 245-296, 2004
- (with H. Yamada) "Decomposition of the lattice vertex operator algebra $V_{\sqrt{2}A_{\ell}}$", Journal of Algebra, 272 (2), 614-624, 2004
- (with M. Kitazume, and H. Yamada) "3-state Potts model, Moonshine vertex operator algebra and 3A-elements of the Monster group", International Mathematics Research Notices, 23, 1269-1303, 2003
- (with N. Lam, and H. Yamauchi) "Extension of unitary Virasoro vertex operator algebra by a simple module", International Mathematics Research Notices, 11, 577-611, 2003
- (with H. Yamada) "$\mathbb{Z}_3$-twisted representations of lattice vertex operator algebras", Communications in Algebra, 31 (6), 3001-3020, 2003
- (with M. Kitazume, and H. Yamada) "Moonshine vertex operator algebra as L(1/2,0) × L(7/10,0) × L(4/5,0) × L(1,0) -modules", Journal of Pure and Applied Algebra, 173 (1), 15-48, 2002
- (with M. Kitazume, and H. Yamada) "A class of vertex operator algebras constructed from $\mathbb{Z}_8$-codes", Journal of Algebra, 338-359, 2001
- "Induced modules for orbifold vertex operator algebras", Journal of Mathematical Society of Japan, 53 (3), 541-557, 2001 , Link
- "Fusion rules for Hamming code vertex operator algebra", Communications in Algebra, 29 (5), 2125-2145, 2001
- (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}D_n}$", Communications in Contemporary Mathematics, 3 (1), 137-151, 2001
- "Representations of ternary code vertex operator algebras", Communications in Algebra, 29 (3), 951-971, 2001
- "Some twisted modules for framed vertex operator algebras", Journal of Algebra, 231, 331-341, 2000
- (with K.Kitazume, and H. Yamada) "Decomposition of the Moonshine vertex operator algebra as Virasoro modules", Journal of Algebra, 226, 893-919, 2000
- (with H. Yamada) "$\mathbb{Z}_2\times \mathbb{Z}_2$ codes and vertex operator algebras", Journal of Algebra, 224, 268-291, 2000
- (with C. Dong,and H. Yamada) "Decomposition of the vertex operator algebra $V_{\sqrt{2}A_3}$", Journal of Algebra, 222, 500-510, 1999
- "Code vertex operator algebras under coordinates change", Communications in Algebra, 27 (9), 4587-4605, 1999
- "Twisted repesentations of code vertex operator algebras", Journal of Algebra, 217 (7), 275-299, 1999
- "On VOA associated with special Jordan algebras", Communications in Algebra, 27 (4), 1665-1681, 1999
- " Construction of vertex operator algebras form commutative associative algebras", Communications in Algebra, 24 (14), 4439-4460, 1996
- (with K. Harada) "Inverses' of Virasoro operators", Communications in Algebra, 23 (12), 4405-4413, 1995